Machine Learning Summer School (MLSS), Chicago 2009

Geometric Methods and Manifold Learning

author: Mikhail Belkin, Department of Computer Science and Engineering, Ohio State University
author: Partha Niyogi, Department of Computer Science, University of Chicago
published: July 30, 2009, recorded: June 2009, views: 4843

Slides

Slides
0:00	Geometric Methods and Manifold Learning
2:37	High Dimensional Data
9:00	Geometry and Data: The Central Dogma
11:08	Manifold Learning
17:15	Formal Justification
22:28	Take Home Message
23:17	Principal Components Analysis
27:45	Manifold Model
28:52	An Acoustic Example (1)
30:44	An Acoustic Example (2)
31:52	Solutions
32:56	Acoustic Phonetics
34:41	Vision Example
38:00	Robotics
39:38	Manifold Learning
40:08	Differential Geometry
40:10	Manifold Learning
40:49	Differential Geometry
41:02	Embedded manifolds
41:46	Tangent space
42:24	Tangent vectors and curves (1)
42:41	Tangent vectors and curves (2)
43:41	Tangent vectors as derivatives (1)
43:57	Tangent vectors as derivatives (2)
45:30	Riemannian geometry
46:21	Length of curves and geodesics
47:25	Gradient
48:52	Exponential map
50:27	Laplace-Beltrami operator
56:21	Intrinsic Curvature
57:10	Dimensionality Reduction
64:37	Algorithmic framework (1)
65:24	Algorithmic framework (2)
66:04	Algorithmic framework (3)
66:20	Isomap
68:34	Multidimensional Scaling (1)
70:56	Multidimensional Scaling (2)
72:04	Isomap
73:32	Unfolding flat manifolds
74:36	Locally Linear Embedding (1)
75:48	Locally Linear Embedding (2)
76:54	Laplacian and LLE
77:41	Laplacian Eigenmaps (1)
78:41	Laplacian Eigenmaps (2)
81:24	Laplacian Eigenmaps (3)
82:38	Diffusion Distance
85:28	Diffusion Maps
87:29	Justification
90:09	A Fundamental Identity
90:44	Embedding
90:51	PCA versus Laplacian Eigenmaps
93:18	On the Manifold
94:25	Curves on Manifolds
94:26	Stokes Theorem
94:58	On the Manifold
95:23	Curves on Manifolds
95:26	Stokes Theorem
98:43	Manifold Laplacian
99:29	Properties of Laplacian
100:44	The Circle: An Example
105:07	From graphs to manifolds (1)
105:10	From graphs to manifolds (2)
105:12	Estimating Dimension from Laplacian

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